AXIMA CANDIDA
Christian all bis life. As his biographer (Dedekind) states, fcHe
reverently avoided disturbing the faith of others; for him the
main thing in religion was daily self-examination'. By the end
of his Gymnasium course it was plain even to Riemann that
Great Headquarters could have but little use for him as a router
of the devil, but might be able to employ him profitably in the
conquest of nature. Thus once again, as in the cases of Boole
and Kummer, a brand was plucked from the burning, ad
major em Dei gloriam.
The director of the Gymnasium, Schinalfuss, having ob-
served Riemann's talent for mathematics, had given the boy
the run of his private library and had excused him from attend-
ing mathematical classes. In this way Riemann discovered his
inborn aptitude for mathematics, but his failure to realize
immediately the extent of his ability is so characteristic of his
almost pathological modesty as to be ludicrous.
Schmalfuss had suggested that Riemann borrow some
mathematical book for private study. Riemann said that would
be nice, provided the book was not too easy, and at the sugges-
tion of Schmalfuss carried off Legendre's Theorie des Xombres
(Theory of Numbers). This is a mere trifle of 859 large quarto
pages, many of them crabbed with very close reasoning indeed.
Six days later Riemann returned the book. *How far did you
read?' Schmalfuss asked. Without replying directly, Riemann
expressed his appreciation of Legendre's classic* 'That is cer-
tainly a wonderful book. I have mastered it.' And in fact he
had. Some time later when he was examined he answered
perfectly, although he had not seen the book for months.
Xo doubt this is the origin of Riemann's interest in the riddle
of prime numbers. Legendre has an empirical formula estimat-
ing the approximate number of primes less than any pre-
assigned number; one of Riemann's profoundest and most
suggestive works (only eight pages long) was to be in the same
general field. In fact "Riemann's hypothesis', originating in his
attempt to improve on Legendre, is to-day one of the out-
standing challenges, if not the outstanding challenge, to pure
mathematicians.
To anticipate slightlys we may state here what this hypotfce-
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